On December 22, 1887 — 127 years to this day which is celebrated as National Mathematics Day in India — Srinivasa Ramanujan, one of the greatest mathematicians the world has seen, was born in Erode in Tamil Nadu. His story, known to many of us, was one of struggle against prejudice, racial discrimination and even illness, to which he eventually succumbed in his early 30s. But within this short span, he had come up with so many interesting questions that mathematicians are trying to solve even today. And that is not all. Many of his proven results and their offshoots are being used in ways that he may not have even envisaged.
While he lived, Ramanujan did not imagine that his work would be applied anywhere. His interest was only in studying mathematics for the pleasure derived in advancing a frontier of thought in the subject. Certainly, working in mathematics takes a lot of discipline and effort, but for those inclined to put in this effort, the rewards are many.
Mathematics and musicThe best way to approach mathematics is by working out problems. Ramanujan, in fact, taught himself mathematics by working through Carr’s “Synopsis,” a book used by Cambridge mathematicians to train their undergraduates. This should inspire those interested in mathematics to go forth and attempt to work through problems and thereby understand the subject at its core.
In a way, learning mathematics is not unlike learning music. While it is good to listen to music in order to understand it, training under a good teacher ensures that more meaning emerges.
Mathematics is not a finished product in which everything has already been worked out. But that is the way it is presented in many schools and colleges. This leaves the student as an observer rather than an active participant. This could also contribute to a feeling of fear about mathematics. But the important thing to keep in mind is a statement attributed to Virgil — “They can who think they can.” As in anything, this applies to mathematics too.
The real rewardRamanujan did not really worry about where his mathematics would be applied when he wrote down his theorems and conjectures. To him, doing mathematics was its own reward. However, today, as we grapple with Internet security, it is number theory and algebraic geometry that are used in cryptography that come to the rescue. Even compressing data to be used in a compact disk or digital video disk requires abstract algebra, field theory and theory of finite Fourier transforms.
So, while applications will follow at some point, they are more like spin-offs of a research. Pure mathematics did not arise with applications in mind but because there was intrinsic beauty to the structure of numbers and their properties. Just like physicists study atoms and molecules and the underlying phenomena, mathematicians study prime numbers and their properties. “This study gives rise to new branches of mathematics, and it is a nice coincidence that much of the work developed in the past, largely motivated by aesthetic considerations, ends up having profound applications in the modern world today,” says Dr Ram Murty, an Indo-Canadian mathematician.
This sense of beauty is important to cultivate. In other words, an appreciation of mathematics is an important aspect of learning mathematics. But how does one appreciate mathematics when it evokes a fear, as it happens with many? “There are at least three factors for math phobia,” says Ram. “The mass hypnosis that math is difficult; the fact that higher math requires the mind to be trained in logical thinking and, at the highest level, that math involves abstract thought, which is usually difficult for many.” To a large extent, conquering the above requires two approaches. One would be to work in the area of your interest and not be influenced by ideas that it may be too difficult, and the other is to make the effort, work on problems, read about mathematics and cultivate an appreciation of the subject.
The life of a mathematician is one of struggle, groping in the dark, pondering and pausing, striving to develop a perspective. But it also holds moments of discovery, surprise, pleasure and promise. The path may not be smooth but there is never a dull moment.
